# Extensional (elongational) viscosity.

I have been asked about extensional viscosity and its measurement. Before I discuss these subjects, I need to point out that when we measure or specify viscosity in the coatings industry, we virtually always are dealing with shear viscosity and laminar flow. Processes such as brushing, spraying, roll coating, pipe flow, and pigment dispersion involve shearing deformation such that one layer of material slides over another and over the substrate, pipe, or pigment particle. When measured under the right conditions with devices such as flow cups and rotational viscometers, shear viscosity enables us to meet specifications and predict or confirm that our coatings will apply properly, flow and level adequately and not sag noticeably.

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However, there is another type of viscosity called extensional or elongational viscosity. Extensional flows occur when fluid deformattion is the result of a stretching motion. Well known examples of such flows include the spinning of fibers for textiles, extrusion of polymer melts, and blow-molding of plastic bottles. Stretching also occurs in coatings, particularly during the breakup of droplets in spray atomization, the splitting of paint between a brush and the substrate, and the splitting of paint between the roller and the substrate in roll coating (architectural and industrial coatings). Less obvious stretching undoubtedly occurs in sagging and surface tension driven flows. Unlike shear viscosity, extensional viscosity has no meaning unless the type of deformation is specified. The three types of extensional viscosity are uniaxial, biaxial, and pure shear. However, uniaxial viscosity is the only one used to characterize fluids. For a Newtonian fluid, the uniaxial extensional viscosity is three times the shear viscosity: [([[eta].sub.e]).sub.uni]= 3[eta] and for non-Newtonian fluids it can be many times higher.

Extensional viscosity is related to the stress required for the stretching. This stress is defined as that necessary to increase the distance between two material entities in the same plane when the separation is s and the relative velocity is ds/dt The deformation rate is the extensional strain rate, which is given by the equation e = 1/s (ds/dt).

The problem with the extensional viscosity of paints and inks is that it is difficult to measure.

Historically, extensional viscosity measurements have been done on polymer melts and concentrated solutions with homemade instruments. Commercial instruments have come and gone and one or two are currently available. Most devices stretch a filament at a constant deformation rate and measure the force necessary to do so along with the diameter of the filament. The methods are limited to spinnable fluids, which do not include paints and inks unless they are highly thickened. However, a number of adhesives and sealants probably could be tested with these instruments. Two rheometers that may hold promise for measuring extensional viscosities of paints and inks are the Haake Capillary Breakup Extensional Rheometer (CaBER 1) and the Vilastic V-E Rheometer with the extensional viscoelastic attachment. They both claim wide shear viscosity ranges that go down to 5-10 mPa*s (cPs), which should allow testing of just about all paints and inks. Unfortunately, I have never had the opportunity to work with either one of these instruments and have not yet seen any paint or ink data from them.

With such measurement difficulties, why should we worry about extensional viscosity, much less try to measure it? It turns out that high extensional viscosity contributes to roller spatter, roll coat ribbing and misting, poor spray atomization (large droplets, stringing, and cobwebbing) and poor knitting of spray droplets on the work piece. Extensional viscosity is related to viscoelasticity, so one way to get at extensional viscosity is to measure or estimate the degree of elasticity of the fluid. Measurement of viscoelasticity is not easy either and requires an oscillatory rheometer for precise measurements, but a lot can be learned from careful observations during rheoiogical measurements and paint formulation. For example, a viscoelastic fluid tends to push up the cone of a cone/plate viscometer or cause chattering (bouncing) of the cone. It also is liable to climb up stirrer shafts during polymerization or mixing and during viscosity measurement in a concentric cylinder viscometer. A viscoelastic fluid shows extrusion swell from a syringe that can be observed by eye or, better, with a microscope. What causes viscoelasticity? In solvent-borne coatings, it is likely to be high molecular weight resin, often just a small amount that shows up in gel permeation chromatography (GPC) as a high MW "tail." Waterborne coating elasticity also may be due to high MW material or to solvent swelling of the latex or dispersion resin. Relevant references include J.E. Glass, J. Coat. Technol., 50(641), 56(1978); D.A. Soules, R.H. Fernando, and J.E. Glass, J. Rheol., 32, 181, 199(1988); and K. Niedzwiedz et al, Applied Rheol., 19(4), 41969-1(2009).

By Clifford K. Schoff, Schoff Associates
COPYRIGHT 2011 American Coatings Association, Inc.
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